Question

The illumination lights in an operating room use a concave mirror to focus an image of a bright lamp onto the surgical site. One such light uses a mirror with a 30 cm radius of curvature. If the mirror is 1.2 m from the patient, how far should the lamp be from the mirror?

Short answer

The distance of lamp from the mirror is 17 cm.

Step-by-step solution

Step 1. Given information is :Mirror is concaveRadius of curvature of mirror R = 30 cmDistance between mirror and the patient = 1.2 m

We need to find out the distance of lamp from the mirror.

Step 2. Finding Focal length and then using Mirror Formula.

Focal Length :

$$\begin{gathered} f=\frac{R}{2} \\ f=\frac{30cm}{2} \\ f=15cm \end{gathered}$$

Using Formula :

$$\begin{gathered} \frac{1}{s}+\frac{1}{s\text{'}}=\frac{1}{f} \\ \frac{1}{s}=\frac{1}{f}-\frac{1}{s\text{'}} \\ \frac{1}{s}=\frac{s\text{'}-f}{fs\text{'}} \\ s=\frac{fs\text{'}}{s\text{'}-f} \\ s=\frac{(15cm)(120cm)}{120cm-15cm} \\ s=17cm \end{gathered}$$